Meaning: a stately court dance in the 17th century
To the eye of an uninitiated observer, the pair might be dancing a few of the more open figures of the minuet.
At length she produced a little something to my joy. Then I made her finish the minuet, i.e. only the first voice.
Thereupon I wrote four measures of a minuet and said to her: 'Now look what an ass I am; I have begun a minuet and can't finish even the first part; be good enough to finish it for me.' She thought it impossible.